Question: Find the greatest common factor of $60$ and $60$.
The greatest common factor (GCF) is the largest number that is a factor of $60$ and $60$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}60 &=2\cdot2\cdot3\cdot5\\\\\\\\ 60 &=2\cdot2\cdot3\cdot5 \end{aligned}$ The results are the same because $60$ and $60$ are the same number! Since $60=60$, the factors that are common to each number are the same: $ \begin{aligned}60 &=2\cdot2\cdot3\cdot5\\\\\\\\ 60 &=2\cdot2\cdot3\cdot5 \end{aligned}$ Both numbers share all of their factors ${2}$, ${2}$, ${3}$, and ${5}$, so the GCF is $2\cdot2\cdot3\cdot5={60}$. The greatest common factor of $60$ and $60$ is $60$. In general, the greatest common factor of any number and itself is that number.